Rehybridization dynamics into the pericyclic minimum of an electrocyclic reaction imaged in real-time

Electrocyclic reactions are characterized by the concerted formation and cleavage of both σ and π bonds through a cyclic structure. This structure is known as a pericyclic transition state for thermal reactions and a pericyclic minimum in the excited state for photochemical reactions. However, the structure of the pericyclic geometry has yet to be observed experimentally. We use a combination of ultrafast electron diffraction and excited state wavepacket simulations to image structural dynamics through the pericyclic minimum of a photochemical electrocyclic ring-opening reaction in the molecule α-terpinene. The structural motion into the pericyclic minimum is dominated by rehybridization of two carbon atoms, which is required for the transformation from two to three conjugated π bonds. The σ bond dissociation largely happens after internal conversion from the pericyclic minimum to the electronic ground state. These findings may be transferrable to electrocyclic reactions in general.


Note 2, Structural Signatures of aTP Rotamers
αTP exhibits a total of three ground state conformers, which differ by the rotation of the isopropyl group around the bond connecting it to the ring (M, P, and T in Supplementary Figures 5 and 6).
Supplementary Figure 5 shows the simulated PDFs as well as the carbon coordination sphere contributions for each of the rotamers compared to experiment. The most significant difference between the experimental and simulated PDFs in Supplementary Figure 6a is the magnitude of the minimum at 3.5 Å, which is connected to the bimodal distribution in the third carbon-carbon coordination sphere. The reasons for these differences are differences in orientation of the (C7) and (C8) carbon atoms with respect to the ring plane. In the M and P rotamers, one of the carbons is signal. In general, the rotamers undergo similar dynamics and the amplitudes of the peaks and troughs match well. According to panel d, ΔPDFs of the rotamer m/p are almost identical and the main difference is from t at the pair distance between 3 and 5 Å. However, the difference from the different rotamers cannot be distinguished from the experimental measurement.

Note 3, Error Function Fits to Temporal Onsets of the ΔPDF Signal in regions α, β, and γ
We characterize the temporal onset of the integrated ΔPDF Signal the α, β, and γ regions by fitting an error function  Supplementary Table 1.

Note 4, Conrotatory Hydrogen Motion
The evolution of the excited state wavepacket of αTP within the first 80 fs in conrotatory movement of the hydrogens around the (C3) and (C4) carbons is depicted in Supplementary Figure   9 (coordinate defined in the caption and in Ref. 1

Note 5, Conrotatory Planarization and Deplanarization Motions
The amplitudes of the individual planarization motions (green and purple curves in Fig. 4b) show close to identical amplitudes, whereas the corresponding deplanarization motions in Fig. 4c show a stronger amplitude for the deplanarization motion involving the methyl group. The behavior is To account for the changes in the total electron number in each pulse, each diffraction pattern (or image) is normalized to the total signal in the ranges of 2 < s < 8 Å -1 .

Diffraction Percentage Difference:
We optimize our analysis of the experimental data by evaluating diffraction percentage difference signals. The 1-dimensional scattering intensity as a function of s, "#$ ( ), is obtained by azimuthally averaging the 2-dimensional diffraction pattern using the determined centers. To highlight the time-dependent changes in the data, we calculate the percentage difference signal according to the following equation, where "#$ ( , ) is the total scattering intensity for each pump-probe delay time, t. The reference signal "#$ ( , < 0) is obtained by averaging the diffraction signal measured at delays -2 ps < t < -500 fs, which corresponds to the static, unpumped scattering signal. Supplementary Fig. 10 shows a false-color plot of the experimental % show several representative delay-slices of the measured signals (curves) and uncertainty (shaded areas) at specific pump-probe delays before and after a further background removal process, respectively. In this process, a low-order (up to 2nd order) polynomial is fitted over the whole s range. 4,6 This procedure has little effect on the low s region, but significantly helps to reduce noise and systematic offsets at high s (see Supplementary Figure 11). We applied a standard bootstrapping analysis to estimate the statistical uncertainty of the measurement. In total, the data set contains 145 runs, and a single run contains diffraction patterns at each individual delay. We by following the equations below, where "#$ ( , ) is the delay dependent modified scattering intensity, 4)1 ( ) the atomic scattering, 5 ( ) is the scattering amplitude of the )0 atom calculated using the ELSEPA program. 9 The Δ of the measurement is then obtained by applying a sine transform of the "#$ ( , ) following the equation below: where represents the pair distance in real space, κ is the damping constant and ;4# the Eq. 6 consists of two terms, in which

Note 7, ɑTP Photoinduced Ring-Opening Dynamics
Excited State Dynamics on S1: The photoinduced ring-opening of aTP follows very closely to its parent molecule, CHD. Like CHD, the S1 and S2 adiabats in the FC region of aTP exhibit the diabatic character of a single and double electron excitation from its highest occupied molecular orbital (HOMO) to its lowest unoccupied molecular orbital (LUMO), respectively (see CI coefficients in min S0 in the Supplementary Data). The S1 adiabat changes character as the wavepacket evolves away from the FC region (See CI coefficients in S0/S1 MECI in the Supplementary Data), implying there is a CI between S2 and S1. As we have shown in our previous work, the S2/S1 CI is considerably sloped and will be almost avoided entirely by the wavepacket as aTP evolves towards the S0/S1 CI. Therefore, we are confident that aTP's relaxation mechanism can be described in its entirety within two adiabatic states. For this reason, all three rotamers of aTP were placed on S1 to simulate its photoinduced ring-opening and the subsequent ground state isomerization dynamics in isolation for the first 1 ps.
All three rotamers of αTP show essentially identical photoinduced ring-opening dynamics and resemble CHD quite closely. Supplementary Figure 5a shows the population dynamics of all three rotamers as TBFs are spawned and population is transferred from S1 to S0. The decay constant for the photoinduced ring-opening process is 168 +/-22 fs when averaged over all 60 ICs, which is slightly slower than CHD (139 +/-25 fs) and faster than aPH (~456 +/-115 fs (axial) and 285 +/-71 fs (equatorial)). The orientation of the isopropyl group does not seem to influence the decay time ( Supplementary Figure 5a). Furthermore, Supplementary Figure 5b shows that population transfer events mainly take place in the first 200 fs of dynamics when the C3-C4 distance is elongated past 1.8 Å as the wavepacket traverses through the S0/S1 CI. Supplementary Figure 5c shows that the majority of spawning geometries are quite similar in structure and energy (within 0.1 eV) to the ring-open MECI. Therefore, we treat all rotamers on an equal footing when computing observables from the AIMS dynamics.
aTP strictly relaxes through the ring-opening nonradiative relaxation pathway via a conrotatory fashion. Supplementary Table 2 shows the branching ratio from all 60 ICs between the closed-and open CIs, with effectively 100% of the wavepacket reaching the S0/S1 CI. This allows us to directly follow the conrotatory and disrotatory ring-opening motion for the entire wavepacket. Supplementary Figure 9 shows the projection of the wavepacket population onto conrotatory and disrotatory angles (see Supplementary Figure 9 inset) for the first 80 fs of the excited state dynamics. Increasing conrotatory/disrotatory angle means the ring opens in a conrotatory/disrotatory fashion. After excitation, the conrotatory angle increases dramatically, while the disrotatory angle remains relatively small. When the wavepacket reaches the S0/S1 CI, it can either return to the photoreactant aTP or go on to form the photoproduct cZc IPMHT. As is the case with CHD, the S0/S1 CI is relatively peaked for all rotamers of aTP (Supplementary Figure   17). Supplementary Table 2 shows that approximately 42 +/-4 % of the wavepacket results in the formation of aTP while 58 +/-4 % forms cZc-IPMHT. This relatively split branching ratio can be attributed to the peak-like of the S0/S1 CI. Within the bootstrapped error bars, we found no single rotamer to be remarkably different.

Ground State Dynamics on S0:
The natural evolution of the wavepacket dynamics on the ground state can be followed by binning geometries along ground-state TBFs into one of the αTP photoproducts ( Fig. 1). Following previous studies, 3 The population transfer is defined as the total population transferred to a child TBF from the beginning of coupled propagation until the child TBF becomes completely uncoupled (off-diagonal elements in the Hamiltonian become small). b) The population of the wavepacket on the S1 adiabat for the first 800 fs of the photodynamics of aTP. Decay constants from single-exponential fits along with bootstrapped errors are shown in the inset. c) Histogram of the population transfer vs the energy gap of all S1/S0 spawning geometries from the AIMS simulation for all three rotamers. Spawning geometries superimposed on their respective ring-opening MECI are shown in the inset with all hydrogens (except for the isopropyl) removed for clarity. Figure 6. Pair distribution functions of αTP ground state rotamers. Panel a plots both the experimental and simulated ground state pair distribution functions. The simulated PDF(r) include all the three rotamers. The difference of PDF(r) between rotamer M and P is rather small and only rotamer T displaces certain amount of difference at the 3rd and 4th coordination shells. The colored shaded areas underneath the PDF curves reflect the relevant contribution from carbon-carbon atomic pairs in each different carbon coordination spheres from all the three rotamers. The shading plots in panel b reflect the contribution of carbon coordination spheres from each individual rotamers.